Subgroups — #13092523

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic
2	#10625058	C₂	1	2	yes	maximal
3	C₂₃×#106	C₂	1	1	yes	maximal, characteristic
4	#10624997	C₂	1	1	yes	maximal, characteristic
5	#10624992	C₂	1	2	yes	maximal
6	C₂×Dic₄₆	C₂²	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
9	Dic₂₃⋊C₄	—	2	2	no	—
10	C₄×Dic₂₃	—	2	2	no	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₉₂	C₄	1	4	yes	complemented
14	C₂×C₄×C₂₃	—	2	2	no	—
15	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₃	—	2	2	no	—
17	C₂×Dic₂₃	D₄	1	2	yes	—
18	Dic₄₆	—	2	2	no	—
19	Dic₄₆	C₂×C₄	1	4	yes	—
20	C₈×C₂₃	C₂×C₄	1	2	yes	—
21	C₂₃⋊C₈	—	2	1	no	—
22	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₂₃	—	4	2	no	—
24	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₃	#41	1	1	yes	characteristic
26	Dic₂₃	—	2	4	no	—
27	Dic₂₃	—	2	2	no	—
28	#441	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
30	C₂×C₂₃	#137	1	2	yes	—
31	C₂×Q₁₆	—	23	1	no	—
32	C₄×Q₈	—	23	2	no	—
33	#106	D₂₃	1	1	yes	characteristic
34	#103	—	23	2	no	—
35	#97	—	23	1	no	—
36	C₂₃	#441	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	23	2	no	—
38	Q₁₆	—	23	4	no	—
39	C₂×C₈	—	23	1	no	—
40	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
41	C₄⋊C₄	—	46	2	no	—
42	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
43	C₄²	—	23	1	no	—
44	C₄²	—	46	2	no	—
45	Q₈	—	23	4	no	—
46	Q₈	—	46	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	23	2	no	—
49	C₂×C₄	—	46	2	no	—
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	46	1	no	—
52	C₈	C₄×D₂₃	1	2	yes	—
53	C₂²	D₄×D₂₃	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	46	4	no	—
56	C₄	—	46	2	no	—
57	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
58	C₄	#67292	1	1	yes	characteristic
59	C₂	#10625064	1	1	yes	characteristic
60	C₂	#10625086	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#106	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#106	D₂₃
hypocenter	C₂₃	#441
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. Dic₉₂	C₄	semidirect
36. C₂₃	#441	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₉₂	2
#10625058	2
C₂₃×#106	2
#10624997	2
#10624992	2
#441	23